How can you render out just the audio from a video in VSE?
Blender isn't a good choice if you are only outputting audio, blender will still render an image for each frame. You can delete all objects in the scene and choose blender render or set samples to one with cycles and use a small image size (50x50) to cut the render time.

If you are only extracting the audio from a file, you would be better off not using blender, using ffmpeg in a terminal it is much quicker to copy the audio track from a video without any conversion.

ffmpeg -i vid.mp4 -acodec copy audioonly.mp3


You may also want to use audactity to open the video file and save out the audio.

If you do want to use blender, in the output settings, select ffmpeg video. For container select one that supports multiple codecs, such as mpeg-4 and then for video codec choose No Video (2.7x this shows as None).